Re: Is this an expensive build?
Action truing can run from $200-400 plus depending on what they consider truing. Normally means recutting the threads also.
IMO I would not worry about making it a repeater especially in the 700. Most consider the 700 marginal at best for the Lapua. I would not weaken it any more.
Weld and time the bolt $60-100 or so depending. Hope he does not silver solder only.
Chambering for $175-400 again depending on the smith.
Muzzle brake installed and crown If you supply the brake is $100 or so.
as you did not mention, what bottom metal are you using and did you supply. There will be work there to fit and maybe mill again.
Bedding $100-250 depending on skim or pillars. I would certainly pillar any 338 lapua.